Question

**6.4.4**

Annual rainfalls for Sydney, Australia are given in table #6.4.6. ("Annual maximums of," 2013). Can you assume rainfall is normally distributed?

**Table #6.4.6: Annual Rainfall
in Sydney, Australia**

146.8 |
383 |
90.9 |
178.1 |
267.5 |
95.5 |
156.5 |
180 |

90.9 |
139.7 |
200.2 |
171.7 |
187.2 |
184.9 |
70.1 |
58 |

84.1 |
55.6 |
133.1 |
271.8 |
135.9 |
71.9 |
99.4 |
110.6 |

47.5 |
97.8 |
122.7 |
58.4 |
154.4 |
173.7 |
118.8 |
88 |

84.6 |
171.5 |
254.3 |
185.9 |
137.2 |
138.9 |
96.2 |
85 |

45.2 |
74.7 |
264.9 |
113.8 |
133.4 |
68.1 |
156.4 |

**6.5.2**

A random variable is normally distributed. It has a mean of 245 and a standard deviation of 21.

- If you take a sample of size 10, can you say what the shape of the distribution for the sample mean is? Why?
- For a sample of size 10, state the mean of the sample mean and the standard deviation of the sample mean.
- For a sample of size 10, find the probability that the sample mean is more than 241.
- If you take a sample of size 35, can you say what the shape of the distribution of the sample mean is? Why?
- For a sample of size 35, state the mean of the sample mean and the standard deviation of the sample mean.
- For a sample of size 35, find the probability that the sample mean is more than 241.
- Compare your answers in part c and f. Why is one smaller than the other?

Answer #1

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